Rewrite as a simplified fraction. ${0.2\overline{90} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 290.909...\\ 10x &= 2.909...\end{align*}}$ Subtracting the two equations, we have: ${990x = 288}$ ${x = \dfrac{288}{990}} $ ${x = \dfrac{16}{55}} $